Other efforts were more concerned with efficiency and synthesis quality than interpretable representations of texture. To better model higher order dependence between features De Bonet [1]} proposed matching the conditional distribution of the finest level of pyramid coefficients based on all 'parent' coefficients (i.e. pyramid coefficients at roughly the same spatial location in coarser levels), leading to an auto-regressive coarse to fine synthesis algorithm. Many later works would propose refined auto-regressive synthesis strategies. Efros and Leung [2]} proposed sampling the output pixel-by-pixel at a single scale by conditioning on a large patch 'on the scale of the biggest regular feature', and iteratively 'growing' the synthesized texture from a small patch randomly taken from the exemplar. Wei and Levin [3]} proposed another auto-regressive procedure with elements of the approaches taken by [1]} and [2]}, synthesizing the texture coarse to fine, but within a scale
synthesizing in raster-order; conditioning on both context from the coarser scale and on already synthesized pixels within the same scale. Ashikhmin [6]} extended the algorithm of [3]}, and proposed replacing a global search for matching conditioning structures in the texture exemplar with selecting regions with a consistent offset to those already sampled, resulting in synthesized textures consisting of large irregular regions of the texture exemplar. Harrison [8]} proposed a more principled method for choosing the order in which pixels should be sampled, hypothesizing that the sampling order should be based on the minimizing the entropy of the pixel distribution to be sampled (sample pixels which will be well explained by the synthesized texture so far) normalized by entropy of the neighborhood sampled from in the texture exemplar (to prevent only sampling texture from highly structured regions of the texture). Hertzmann et al. [9]} proposed an extension of the pixel-by-pixel method of [6]} which allowed trading off between matching coherent regions as proposed by Ashikhmin (i.e. cloning large regions of the exemplar, which preserved details well but could introduce seams between cloned regions) and the l2 appearence matching of [3]} (which was less prone to seams, but synthesized blurrier results), in many cases achieving results with the best properties of both algorithms.
